Integral averages of two generalizations of the Poisson kernel by Haruki and Rassias (Q936984)

Summary: In 1997, \textit{H. Haruki} and \textit{T. M. Rassias} [J. Appl. Math. Stochastic Anal. 10, No. 2, 191--196 (1997; Zbl 0892.31001)] introduced two generalizations of the Poisson kernel in two dimensions and discussed integral formulas for them. Furthermore, they presented an open problem. In 1999, Kim gave a solution to that problem. Here, we give a solution to this open problem by means of a different method. The purpose of this paper is to give integral averages of two generalizations of the Poisson kernel, that is, we generalize the open problem.